An apparatus and a method of the type defined in the opening paragraph are known from patent specification U.S. Pat. No. 3,789,203, which describes a function generator employing approximation by iterative interpolation. Said apparatus is intended for data processing applications which require a calculation of functions such as, for example, sin(x), tan(x). This apparatus requires only a minimal storage capacity from a user device. Starting from two pints belonging to a function to be interpolated the method first interpolates the function by a straight line between the two points and then performs an approximation to deviations between the straight line and the function by polynomial approximations of increasing order. Subsequently, it replaces the initial points by approximate points in order to reduce the length of the segment between the points to be processed and, finally, it repeats the preceding operations.
Such a method requires extensive computing means and can be carried out only by means of powerful computers.
There are applications for which such a method cannot be employed because the available means are not adequate. Moreover, for certain uses it may be satisfactory to perform an approximate calculation of the function for a limited number of values of the independent variable.
This may concern a sigmoid function applied to neural potentials supplied by at least one neuron in a neural network. It may concern another non-linear function, for example a root function, for calculating distances between neuron states. The applications may also involve other devices such as function generators, computing devices and the like.
To calculate such a function without resorting to an approximation function various other ways can be used.
The exact mathematical calculation can be performed for each value of the independent variable to be processed by programming a computer by known methods. Such a method requires that each time the same operations are carried out, which may take a long time if the number of values is large.
It is also possible to store pre-calculated tables in a memory. The result can then be read rapidly from the memory. However, to cover all the possible values of the independent variable with an adequate resolution tables with a very high capacity are required. Consequently, these computing methods have disadvantages.
On the other hand, it may be required to identify two variables which are related to one another by pairs of values associating a dependent variable with an independent variable. Thus, in monitoring an industrial process it may be required to measure, for example, an efficiency R of an operation as a function of the temperature T at which this operation R=f(T) is performed. To monitor the process batches of measurement pairs may be plotted in a graph. This may be effected to characterise the process or to derive new control parameters for said operation. This is described, for example, in the article by H. ISHIBUCHI and H. TANAKA, "Regression analysis with interval model by neural networks" in "IEEE International Joint Conference on Neural Networks", vol. 2, 18-21 November 1991, SINGAPORE. These new parameters should be representative of the basis of said operation and measurement fluctuations inherent of this type of process should be ruled out. It is therefore desirable to determine an approximation of the function f(.).
Thus, in a given case this may involve measurements which are erratic or afflicted with errors to be represented by an approximation function.
In another case accurate values are available but their envisaged use does not require a high accuracy and an approximation function will be adequate.